Let M be a non-empty set endowed with a dense linear order without the smallest and greatest elements. Let (G,+) be a group which has a non-trivial uniquely divisible subgroup. There are given conditions under which every solution F: M×G → M of the translation equation is of the form for a ∈ M, x ∈ G with some non-trivial additive function c: G → ℝ and a strictly increasing function f: M → ℝ such that f(M) + c(G) ⊂ f(M). In particular, a problem of J. Tabor is solved.
@article{bwmeta1.element.bwnjournal-article-apmv64z3p207bwm,
author = {Janusz Brzd\k ek},
title = {On the increasing solutions of the translation equation},
journal = {Annales Polonici Mathematici},
volume = {63},
year = {1996},
pages = {207-214},
zbl = {0860.39035},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv64z3p207bwm}
}
Janusz Brzdęk. On the increasing solutions of the translation equation. Annales Polonici Mathematici, Tome 63 (1996) pp. 207-214. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv64z3p207bwm/
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